Appendix I. Sample of Countries

MEXICO

Sample of Countries Latin America Asia Emerging Europe Other Argentina India Belarus Turkey Brazil China, Mainland Kazakhstan South Africa Chile Indonesia Bulgaria Israel Colombia Republic of Korea Russian Federation Mexico Malaysia Ukraine Peru Pakistan Czech Republic Uruguay Philippines Slovak Republic Venezuela, Rep. Bol. Thailand Estonia Latvia Hungary Lithuania Croatia Slovenia Poland Romania

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Appendix II. Regression Results – EM Bond Factor

(1) (2) Full Sample Post crisis

vix -0.0465*** -0.0635*** (0.0122) (0.0116) wti 0.0106*** 0.00836* (0.00255) (0.00457)

L.adv_growth -0.0708* -0.0616 (0.0393) (0.0861) L.bric_growth 0.0712*** 0.339*** (0.0259) (0.0545) fed funds 0.241 -1.985 (0.195) (4.319) _cons -0.113 -1.040** (0.350) (0.391)

N5924 R-sq 0.519 0.749

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WELFARE GAINS FROM HEDGING OIL-PRICE RISK1

Since at least 2001, Mexico’s federal government has hedged the near-term fiscal impact of declines in oil prices through put options. Using a structural model calibrated to the Mexican economy, we quantify the overall benefits of this long-standing policy. Compared to a self- insurance alternative, we find welfare gains from hedging through put options equivalent to a permanent increase in consumption of 0.4 percent. These gains arise mostly from a reduction in sovereign spreads and to a lesser extent from smoothing income volatility. In terms of design, expanding the program to cover domestic fuel sales could yield further gains once gasoline and diesel markets are liberalized. Relying more on liquid instruments—such as options on the Brent—is an avenue worth exploring to ensure the program remains cost effective.

A. Introduction

1. Mexico’s hedging program has the objective to hedge the value of Mexican oil exports at a strike price that is consistent with the one assumed in the budget for each year. To meet this objective, the program involves buying Asian put options to insure the price of oil for the whole year. 2 The execution involves purchasing options with Maya oil—a type of Mexican heavy crude oil—and Brent as underlying assets, although the former dominates as Maya oil represents about 80 percent of Mexico’s oil export volumes.

2. The program helped cushion the Cash Flow from Options (In percent of GDP) fiscal impact of the decline in oil prices in 0.7 2009, 2015, and it is expected to do so 0.6 Inflows again this year. Since 2001, the options had Outflows 0.5 a cost, on average, of 0.1 percent of GDP per year, but were exercised only in 2009 and 0.4 2015, yielding payoffs close to 0.6 percent of 0.3

GDP in each occasion. It is expected that the 0.2 options will be exercised again this year, 0.1 yielding estimated revenues for 0.3 percent - of GDP. 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Source: National authorities; and IMF staff calculations.

1 Prepared by Chang Ma and Fabian Valencia. The authors thank Dora Iakova, Alexander Klemm, Damien Puy, Robert Rennhack, Alejandro Werner, seminar participants at the IMF and the Bank of Mexico for comments and suggestions. 2 An American or European put option is exercised if the spot price on a particular day exceeds the strike price. In contrast, an Asian put option is exercised if the average spot price for a pre-determined period, which in the case of Mexico is one year, exceeds the strike price. In this way, Mexico guarantees a minimum average price of oil for the whole fiscal year.

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3. This paper examines the welfare gains for Mexico from having the hedging program. Using a structural model, this paper asks three questions: 1) how large are the welfare gains from using put options to hedge oil price risk; 2) what are the main channels through which these gains operate; and 3) what design considerations can increase the benefits of the program further.

B. Model Setup

4. The model summarizes a small open economy with representative consumers who receive income from oil and non-oil sources and consume a tradable good. The model is a standard sovereign default model (Arellano, 2008). It is assumed that a social planner (i.e. the government) makes decisions aimed at maximizing the present discounted value of private agents’ utility derived from consumption ( Ct ):  t EUC0   ()t . t0 Income resembles the structure of fiscal revenues, with oil and non-oil sources. The non-oil sources

(e.g. taxes, denoted ft ) are assumed to evolve deterministically. Oil revenues stem from exports and from domestic sales.3 A fraction  of oil export volume (Q)—assumed fixed—is hedged through put options, which guarantees an oil price at least as good as the strike price p .4

Yfmax{ ppQpQ ,0} dd. (0.1) tt   t    t fiscal revenue non-oil revenue exports domestic sales  Oil Revenue

5. The country purchases put options every year to hedge against a fall in oil prices. The government defaults on its liabilities whenever it is optimal to do so. In other words, the country defaults if

Vpfdc(,) VBpf (,,)maxUC( ))  EVB ( ,p ,f , ttttttt CBtt,11 t ttt1 t1 t1

d c where Vpfttt(,) and VBpftttt(,,)denote the present discounted value of the utility from consumption if the country defaults or not in period t, respectively. VBptttt1111(,,) f denotes the present discounted value of consumption as of the next period (t+1), If the country does not default, the available resources to consume are what remains after receiving revenues Yt , issuing new debt (

3 d Domestic sales are net of imports. The price pt represents an average price across fuels. The model is expressed in constant U.S. dollars. 4 In the model, the central government and the state-owned oil producer, Pemex, are seen as one entity. In practice, the oil hedging program is only intended to hedge the exposure of the central government to oil price risk, given that Pemex has its own independent operation. Pemex currently does not hedge its own revenues.

(continued)

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Bt1 ) at price qt , repaying existing debt, Bt , and purchasing put options to insure Q barrels of oil at a cost of()pt per barrel:

CYBqBttttt 1  Qp() t. (0.2)

If the country defaults, it resorts to autarky but it can still hedge oil price risk.5 In addition to being unable to issue debt, default implies an income loss equal to h.6 In case of default, the resource constraint boils down to

CQptttYh () t. (0.3)

There is, however, a positive probability (  ) that the country exits its default status and issues debt again. This possibility is taken into account in the calculation of the present discounted value of future utility of consumption and hence in the default decision:

d d Vpfttt(,)  UC()ttttEVp ttt(0,,11 f ) (1) EVp tt (11 , f)

6. The price of sovereign bonds and put options is determined in international financial markets by risk neutral investors. The underlying assumption is that international investors hold diversified portfolios and price bonds and options as to ensure an expected return equal to the international risk-free rate ( r* ). Because the ex-ante rate of return on these instruments is the same, the risk-neutral investor is indifferent between holding a bond or being the counterpart of a put option.

EDBpftttt1(,,) 111 qB(,,) p f  , with DB(,,)1 p f  if country defaults (0.4) tt1 tt 1 r* ttt111

Epp[max{ ,0}]  ()p  tt1 (0.5) t 1 r*

7. The model is calibrated to the Mexican economy taking some parameters directly from data and the literature, while estimating others to match chosen data moments. The full model and solution are described in Appendix A. We take from the literature the coefficient of risk aversion. We measure directly in the data the real risk-free interest rate (approximated by the yield on 1-year U.S. treasury bonds deflated with the U.S. GDP deflator); the oil-price process (estimated using an AR1 on the price of the Mexican mix); oil export and domestic sales (net of imports) volumes; the fraction of export volumes hedged; and the deterministic growth rate of non-oil

5 The underlying assumption is that debt and financial derivatives are separate markets.

6 Following Arellano (2008), we assume that income is lower than under no default but it can at most drop to some * value y , which will be calibrated to match sovereign spreads in the data.

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* revenues. The discount factor  and the parameter y of the loss function under default are chosen as to match the government’s gross financing needs and the average Mexican sovereign spread over U.S. treasury bonds. Tables B1-B3 in the appendix show the complete set of parameter values and simulated data moments.

C. Welfare gains and channels

8. The benefits of hedging are computed relative to a self-insurance alternative. Using Monte Carlo simulations, we construct paths for consumption and contrast them with those from a version of the model without hedging.7 In absence of hedging, consumption-smoothing takes place solely through issuing debt. The welfare gains from hedging can be expressed in terms of the permanent increase in consumption that would yield the same present discounted value as in the model with hedging.

9. The estimated welfare gains are equivalent to a 0.4 percent permanent increase in consumption and stem mostly from a reduction in sovereign spreads. These gains are smaller than those reported in Boreinsztein and others (2013)8 but are within the range of estimates found in the literature from issuing catastrophic bonds (0.12 percent, Borensztein and others, 2016) and GDP-indexed bonds (0.46 percent, Hatchondo and Martinez, 2012), which are alternatives to insure against downside risks. 9 Hedging is beneficial in the model because of two channels at work: a reduction in income volatility and a reduction in borrowing spreads. Both are the consequence of lower downside risks from oil-price fluctuations. We decompose the overall welfare gains into these two channels to conclude that about 90 percent of the gains are explained by a reduction in borrowing costs.10 Sovereign spreads are 30 basis points lower, on average, in the model with hedging than in the model with no hedging.

7 The simulation is implemented by initializing the system at some random initial level of debt, B0 , while oil prices are initialized at their unconditional mean. Using the optimal solutions, we simulate 500 paths of 2,000 periods each, for which we compute the average present discounted value of consumption after dropping the initial 500 periods.

8 Boreinsztein and others (2013) report welfare gains from hedging though options (at a one-year horizon) of about 1-percent permanent increase in consumption. In their model, there is no default, while in principle, the option of default can be seen as an insurance mechanism in case of a very negative shock. 9 Lopez-Martin and others (2016) conduct a similar analysis than ours in a sovereign default model in which public and private sector decisions are modeled separately. While they do not directly compute welfare gains, they show that the public sector is willing to pay an important fraction of commodity revenues for options as insurance against declines in oil prices. 10 The decomposition is implemented by solving the model with no hedging using the bond pricing function from the model with hedging. This implies that any remaining welfare gains in this model would be attributed to the income volatility channel.

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D. Design Considerations

10. Sensitivity analysis on the model offers insights for the design of the hedging program. The design of the program requires making decisions on the number of barrels hedged, the strike price, the underlying asset, and the instrument to be used, which ultimately affect the cost of the options. By looking at how the welfare gains change when key parameters of the model are modified we can offer some insights about some of these design questions. In particular, we focus on the size of the program (or volume hedged), the strike price, and the cost of the options.11

Size of the Program

11. The welfare gains increase with the number of barrels hedged. On average, Mexico hedged a range between 210 and 230 million barrels a year during 2010-2015,12 reflecting approximately the volume difference between exports and imports, and representing on average about half of export volumes. For 2017, Mexico increased the volume hedged to 250 million barrels (from 212 million in 2016). The model suggests that it is welfare-enhancing to increase the number of barrels hedged (simulated by varying the parameter  ). Welfare gains peak only after an implausibly large program (9 times exports).

Welfare Gains and Volume Hedged a) Oil Production b) Welfare Gains and Volume Hedged (Millions of barrels) (In percent of consumption) 1600 16 Production Exports 1400 Imports Domestic Consumption 14

1200 12

1000 10 800 8 600 6 400 4 200 2 0 0

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 - 222 444 667 889 1,111 1,333 1,556 1,778 2,000

Source: National authorities; and IMF staff calculations. Percent of Export Volumes

11 Instrument considerations involve first deciding whether buying put options or selling forward are preferable. Boreinsztein and others (2013) show that for hedging horizons of up to 5 years, the welfare gains from selling forward or buying put options are comparable. The choice for Asian options serves the purpose of hedging the average price of oil for the fiscal year in question (see Duclaud and Garcia, 2012 for a description of the Mexican hedging program). 12 The Cuenta publica reports by the Auditoria Superior Federal (Federal Audit Office) provide the cost and volume hedged for each year since 2006.

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12. A larger hedging program can also help reduce volatility of domestic oil revenues once gasoline and diesel markets are fully liberalized. Mexico exports about half of its oil production, while the other half is refined and sold domestically—together with imported oil derivatives—at regulated prices.13 Mexico is gradually liberalizing domestic fuel markets and the process is expected to be completed by 2018. Expanding the hedging program to cover domestic sales, which could be implemented by having Pemex develop its own hedging program, can help smooth the resulting volatility in overall fiscal revenues.

Strike Price

13. The choice for strike price in Mexico has been close to optimal. The choice for the strike price in Mexico is informed by estimates of the long-run price of oil derived from a formula spelled out in the 2006 Fiscal Responsibility Law, which corresponds to a weighted average between historical and futures prices. In the model, this long-run price is the unconditional mean of the estimated AR1 oil-price process. The baseline calibration uses a strike price close to 0.9 times the unconditional mean, which approximates the strike price chosen by Mexico in past years.14 The simulations show that welfare gains peak when the strike price is about equal to the unconditional mean. In practice, this suggests that the choice for strike price in Mexico has been close to optimal.

Welfare Gains and Strike Price

a) Actual Strike Price and Long-run Oil Price 1/ b) Welfare Gains and Strike Price (In USD per barrel) (In percent of consumption) 120 0.7

0.6 100

0.5 80 0.4 60 Baseline 0.3

40 0.2

20 Actual Strike Price Long-run Oil Prices 0.1

0 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 0.7 0.8 0.9 1.0 1.1 2.0 Strike price as a ratio to unconditional mean of oil prices

Source: National authorities and staff estimates. Note: 1/ The long-run oil price is estimated computing the unconditional mean from an AR1 process estimated for each year. The average ratio of the actual strike price to this estimate of the long-run oil price is 0.86. Since in the model the oil price process is time- invariant, we use this ratio to calibrate the strike price. The right figure shows the resulting welfare gains for various strike prices, expressed as a ratio to the unconditional mean, including for the baseline value of 0.86.

13 Pemex is exposed to oil-price risk on both foreign and domestic sales as it receives international prices on the latter. However, additional revenues for the federal government from a wider difference between domestic and international prices partly offset the fiscal impact of oil-price declines. Starting in 2016, fuel excises were fixed at levels close to optimal (IMF 2015) while domestic prices were allowed to move closer in line with international prices. The 2017 economic package envisages liberalizing some markets one-year ahead of schedule with the intention to have fully market-determined prices by 2018. 14 We estimate the AR1 process for oil in 1-year rolling windows. For each year we compute the ratio of the actual strike price (taken from the data) to the unconditional mean from the oil process estimated for that year. The average of this ratio is 0.86, which is used in the baseline model. The calculation also approximates well the moneyness of the options, calculated as the ratio of the strike price to the average futures price for the subsequent year.

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Cost of Options and Base Risk

14. The estimated welfare gains decline if the Welfare Gains and Cost Premiums (In percent of consumption) cost of the options includes a premium above fair 0.5 0.4 price. This premium may stem mainly from non- 0.3 competitive behavior, regulatory constraints, risk 0.2 0.1 aversion, and market illiquidity. The reason for the 0 decline in welfare gains is that the options become -0.1 -0.2 relatively more expensive than debt—the alternative -0.3 instrument used for consumption smoothing— -0.4 -0.5 assuming that debt remains fairly priced. -0.6 0.0 1.0 1.5 2.0 2.5

Source: IMF staff calculations. 15. Relying on liquid instruments such as options on Brent or WTI reduces the likelihood of a Brent - Maya Price Differential (In USD per barrel) cost premium. Given the liquidity and depth of their 25 markets, options on the WTI or Brent are more likely to 20 be fairly priced than less liquid and over the counter 15 10 options with Maya oil as underlying asset. 15 However, 5 the price of Maya oil can deviate significantly from the 0

Brent or WTI, as shown below, implying a tradeoff -5 between covering base risk —defined as unexpected -10 movements in Maya oil price not explained by Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 movements in the Brent or WTI—and reducing the Source:National authorities; and Bloomberg. likelihood of paying above fair price for the options.

16. Base risk could justify a small premium in the cost of options on Maya oil over options on Brent. Since the model does not consider explicitly base risk, some premium above the price of options on Brent may not necessarily be welfare-reducing. An illustrative exercise to quantify base risk, based on estimating rolling AR1 regressions, suggests that negative realizations—defined as a price differential wider than expected—have been concentrated in the US$0-U$5 per barrel range. Furthermore, base risk is mitigated by the fact that forecast errors in the Brent-Maya price differential and in oil prices tend to be positively correlated. 16 Taking this correlation into account, past data suggest only a small probability of a large negative shock in the price differential. In the example below, in only 4.5 percent of occasions the price differential widened unexpectedly more than US$ 3 without any compensation from positive surprises on the price for Brent. In this simple

15 Determining whether options on the Brent and WTI are fairly priced would boil down to knowing with certainty and in real time the underlying data generating process that governs movements in the price of oil. Alternatively, one can adopt the view that given the depth and liquidity of markets for options on Brent or WTI, their prices are as close as feasible to fair price, and any factor leading to a premium above fair price would likely affect the pricing of sovereign debt as well (e.g. a risk-off episode). Since debt is the alternative in the model as a vehicle to consumption smoothing, what matters is whether the premium in option prices is larger than the one in sovereign debt prices. 16 We estimate an AR1 on both, the price differential and the Brent oil price in 5-year rolling windows with monthly data starting in January, 1997. For each window, we generate forecasts for the next 12 months and compute the average out-of-sample forecast error for the 12-month period for each variable.

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©International Monetary Fund. Not for Redistribution MEXICO illustration, a premium of up to US$0.15 per barrel in the price of Maya options over Brent options would imply breaking even between insuring base risk and not.

Base Risk

Probability Distribution Densities Out-of-sample Forecast Errors (In USD per barrel) 0.14 10 Actual Brent-Maya differential 0.12 8 6 0.10 Out-of-sample forecast error in Brent-Maya differential 4 0.08 2

0 0.06 -120 -100 -80 -60 -40 -20 0 20 40 -2

0.04 y = 0.0814x + 1.153 -4 R² = 0.28 0.02 -6 -8 0.00 Forecast error in Maya-Brent differential differential Maya-Brent in error Forecast -10 -11-9-7-5-3-113579111315171921 In US$ per barrel -12 Forecast error in Brent oil prices Source: Bloomberg; and IMF staff calculations.

17. When market conditions imply too high of a premium in Maya over Brent options, base risk could be covered through the FEIP. The price of options on Maya oil may imply at times a premium over options on Brent larger than what exercises like the above suggest. In those circumstances, it may be more cost effective to cover base risk through the Revenue Stabilization Fund (FEIP).17 Mexico has used the FEIP as a complement to the hedging program to insure against negative oil-price shocks. For instance, for 2017, Mexico purchased options with a strike price of US$38 per barrel, when the assumed price in the budget is US$42, with the difference to be covered by the FEIP if needed. A similar approach could be adopted in insuring against base risk.

E. Conclusions

18. Hedging oil-price risk through put options can lead to non-trivial welfare gains relative to self-insurance. In the model presented in this paper, the resulting welfare gains are equivalent to a 0.4-percent permanent increase in consumption and stem mostly from a reduction in borrowing costs for the sovereign.

19. Frequent back-testing exercises to quantify base risk can ensure that the hedging program remains cost effective. Deviations of the price of options from their fair value can lead to lower welfare gains, and one possible source for such a premium is the use of options with Maya oil as underlying asset. Frequent back-testing exercises can provide an up-to-date quantification of base risk to decide on the mix between options on the Maya oil and Brent. Whenever market conditions imply too high of a cost for Maya options over those with the Brent as underlying asset, it may be more cost effective to use the FEIP to cover base risk.

17 The FEIP is a small savings fund intended to smooth the impact of transitory negative shocks on federal fiscal revenues.

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20. A larger program could be beneficial in the context of liberalized domestic fuel markets. So far, the exposure of consolidated public finances to oil-price volatility has stemmed from net exports. Once domestic fuel markets are liberalized, the larger exposure to oil-price volatility can be dealt with a larger hedging program, which could be implemented by having Pemex develop its own hedging program.

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References

Arellano, Cristina, 2008. “Default risk and income fluctuations in emerging economies,” The American Economic Review, 2008, pp. 690–712.

Borensztein, Eduardo, Eduardo Cavallo, and Olivier Jeanne, 2015. “The Welfare Gains from Macro- Insurance Against Natural Disasters,” National Bureau of Economic Research WP#

Borensztein, Eduardo, Olivier Jeanne, and Damiano Sandri, 2013. “Macro-hedging for commodity exporters,” Journal of Development Economics, 2013, 101, 105–116.

Duclaud, Javier and Gerardo Garcia, 2012. “Mexico’s Oil Price–Hedging Program,” in Arezki, Rabah, Catherine Pattillo, Marc Quintyn, and Min Zhu (Editors), “Commodity Price Volatility and Inclusive Growth in Low-Income Countries.” International Monetary Fund, Washington D.C.

Hatchondo, Juan Carlos and Leonardo Martinez, 2012. “On the benefits of GDP-indexed government debt: lessons from a model of sovereign defaults,” Economic Quarterly, 98 (2), 139–158.

International Monetary Fund, 2015. “A Carbon Tax Proposal for Mexico,” Selected Issues Paper, Chapter 4.

Lopez-Martin, Bernabe, Julio Leal, and Andre Martinez Fritscher, 2016. “Commodity Price Risk Management and Fiscal Policy in a Sovereign Default Model,” Bank of Mexico manuscript.

Reinhart, Carmen, Kenneth Rogoff, and Miguel Savastano, 2003. “Debt Intolerance,” Brookings Papers on Economic Activity, 2003 (1), 1–74.

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Appendix I. Model Structure

To simplify the solution of the model, all variables are first normalized by the non-oil income ft , which reduces the number of state variables to 2. The normalized problem, where small variables

C denote normalized values (e.g. c  t ), is shown below: t ft

Value function:

cd Vb(,tt p ) max V (, b tt p ),( V p t )

Value function if there is no default: c1 Vbpc (, ) max t  G1 EVbp(,) tt cbtt,111 1 t t t s.t. cttt q Gb1  QG( pt )  y t Q max{ p - pt , 0}  b t

Value function under default c1 Vpd ()t  G1  EVp(0,)(1)   EVpd ( ) ttttt1 11 st.. ctt y - QG ( p t )- h y t -  QG ( p t )

Price of sovereign bond and put options:

EDbpttt1(,) 11 qb(,) p  tt1 1 r* Epp[max{ ,0}]  ()p  tt1 t 1 r*

The model is solved through value function iteration using a pre-determined grid space for both bt and pt . We start with an initial guess for bond prices qbpi (,) for each bB and pP and

dc the value functions {VbpViii ( , ), ( pV ), ( bp , )}. In each iteration, we find the value for bt1 and

ct within the pre-determined grid that maximizes the value function. The value function and the bond pricing equation are updated and used in the next iteration and so on. The procedure is repeated until the value functions and the pricing equation converge (i.e. when the difference in values between two iterations is small enough that some pre-determined convergence criteria).

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Appendix II. Calibration

Table B. 1 – Parameter Values Parameters Value Source U.S. Real Interest Rate (1-Year Treasury Bill): Risk-free interest rate r*  0.71% 1995-2015 Standard Value in literature Risk aversion   2 Average years in default for Mexico: 1800- Probability of redemption   0.11 2010 (Reinhart, Rogoff, and Savastano, 2009) Unconditional oil price p =48.84 Data Oil price persistence  =0.8403 Data Oil price volatility  =0.2869 Data Export volume (normalized) 1/ Q =0.0047 Data Domestic sales volume (normalized) 1/ Q d =0.0052 Data Strike Price = Data p 0.86* Ep[]t Share of exports hedged  =0.55 Data Domestic oil price d Data log pptt 3.28 0.18log Growth rate of non-oil revenue G= 1.02 Data

Parameter to match moments Discount rate  =0.7182 Model simulation Output loss under default (threshold below * =1.3302 Model simulation which there is no loss) y 1/ Corresponds to model normalized by non-oil income.

Table B.2 Simulated vs. Data Moments Debt ratio 1/ Sovereign spreads In percent Model 51.76 3.51 Data 53.00 3.68 1/ The data counterpart to the debt ratio is the public sector’s gross financing requirements, expressed in percent of non-oil income.

Table B.3 Simulated Moments in Model with and without Hedging Debt ratio 1/ Sovereign spreads Default probability In percent Model with hedging 51.76 3.51 2.54 Model without hedging 49.98 3.82 2.70 1/ The data counterpart to the debt ratio is the public sector’s gross financing requirements, expressed in percent of non-oil income.

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EVALUATING THE STANCE OF MONETARY POLICY1

Using an estimated Taylor rule and a small DSGE model, this study finds that the monetary policy stance in Mexico has shifted from accommodative to broadly neutral.

A. Introduction

1. After a period of an unprecedentedly low policy rate, the monetary policy rate in Mexico was raised by a total of 175 basis points between December 2015 and September 2016. Following a 25 basis point increase in December 2015 (matching the U.S. rate move), interest rates were increased by 50 basis points each during an extraordinary session on February 17 and during regular monetary policy committee meetings on June 30 and September 29, 2016.

2. This paper provides an assessment of the monetary policy stance using various methods. A Taylor rule is used to compare the current policy rate to the rate implied by the estimated historical reaction function. In addition, a small open-economy DSGE model is used to estimate the neutral rate. The main conclusion is that the policy stance has shifted from an accommodative to broadly neutral or mildly restrictive.

B. Estimated Taylor Rule

3. A Taylor rule for Mexico is estimated using monthly data between 2006 and 2016. The ∗ results are presented in equation (1) below, where denotes the policy rate, measures ∗ deviations of inflation from the 3-percent permanent target, measures deviations of 12- ∗ months ahead inflation expectations from the target, is the deviation of output from potential, and to the current level of the Federal Funds Rate. The Federal Fund rate is added to the estimated reaction function since the Bank of Mexico frequently notes that it takes into account the relative monetary stance with the U.S. when setting the policy rate (Mexico and the U.S. have highly synchronized business cycles). It also serves as a proxy for the effect of global interest rates on Mexico’s interest rates. The estimation uses core inflation and one-year ahead expectations of core inflation taken from analysts’ surveys.

∗ ∗ ∗ 3.95 1.25 0.13 0.31 0.30 (1)

4. The estimated Taylor rule captures well the behavior of the Bank of Mexico over the past ten years. An alternative version of the model, with the exchange rate added to equation (1) does not improve the fit further, which suggests that, historically, the Bank of Mexico has not responded to exchange rate changes beyond their impact on current and expected inflation. Changes in the Federal Funds rate explains only a small share of the variance in Mexico’s policy rate, and excluding it does not affect results significantly. Finally, adding a lagged dependent variable -

1 Prepared by Alexander Klemm and Damien Puy.

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©International Monetary Fund. Not for Redistribution MEXICO with an estimated coefficient of 0.88 - to allow for smoothness in policy rate changes, affects the predicted values and the dynamics of the estimated Taylor rule only marginally.

5. The cumulative increase in the policy Taylor Rule vs Actual Policy Rate (In percent) rate over the past year has brought the policy 10 9 Actual rate slightly above the estimated historical 8 Taylor Rule 95% confidence interval reaction function. The tightening is consistent 7 with Bank of Mexico’s message that they are 6 5 tightening pre-emptively to guard against the 4 risk of de-anchoring of inflation expectations in 3 the context of a significant exchange rate 2 depreciation over the past two and a half years. 1 Jul-10 Jul-15 Jan-08 Jan-13 Jun-08 Jun-13 Oct-11 Oct-16 Apr-09 Apr-14 Feb-10 Feb-15 Sep-09 Sep-14 Dec-10 Dec-15 Mar-12 Aug-07 Aug-12 Nov-08 Nov-13 May-11 May-16 C. The neutral interest rate Source: IMF staff calculations

6. The empirical literature suggests that neutral interest rates in advanced economies have declined. Holston and others (2016) estimate neutral rates for the U.S., the euro area, Canada, and the United Kingdom and find a downward trend in neutral interest rates in all four economies. Moreover, they note a substantial co-movement across economies. Pescatori and Turunen (2015) estimate neutral policy rates for the United States, using a methodology that accounts for unconventional monetary policy measures. They also find a strong decline over time. Magud and Tsounta (2012) estimates of neutral interest rates in Latin America also establish a downward trend. The decline in global interest rates has been attributed to an increase in global saving rates related to demographic factors, increased demand for safe assets, low investment rates, and a decline in potential growth rates in a number of large economies. Since Mexico is a small open economy, the reduction in neutral rates in major trading partners is likely to be associated with a decline in Mexico’s neutral interest rate as well.

7. A small open-economy DSGE model is used to estimate the neutral interest rate for Mexico directly. The model consists of a standard IS curve, a Phillips curve, and a Taylor rule. It provides an estimate of the neutral rate, which in this model is the real rate that would prevail if inflation and output gaps were closed.

IS curve: ∗ 0.71 0.70 0.00 (2) where x is the output gap, π is the annualized quarterly (core) inflation rate, r* is the neutral real interest rate, and d is the rate of depreciation.

Phillips curve: 0.48 0.55 0.33 (3) Taylor rule: ∗ 0.19 3 0.17 (4)

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The depreciation of the exchange rate is modeled as an AR(1) process:

0.07 (5)

The neutral interest rate follows a simple process with persistent shocks z.2

∗ 2.72 (6)

3 . 99 (7)

8. The neutral interest rate for Mexico is found to have declined since the mid-2000s. This finding is robust to various changes in the model specification (such as using a Phillips curve based on only on forward-looking inflation), or changes to the data used (replacing core with headline inflation). The results suggest that Interest rates currently the real neutral rate is about (In percent) 10 0.8, although the 90 percent 8 Real neutral rate Real policy rate confidence interval around this estimate is very wide, ranging from - 6

0.5 to 1.8. Moreover, while the finding 4 of a reduction in the neutral interest 2 rate is robust, the exact level of the estimated neutral interest rate, 0 changes with different model -2 specification and shock assumptions. 2001Q1 2001Q4 2002Q3 2003Q2 2004Q1 2004Q4 2005Q3 2006Q2 2007Q1 2007Q4 2008Q3 2009Q2 2010Q1 2010Q4 2011Q3 2012Q2 2013Q1 2013Q4 2014Q3 2015Q2 2016Q1 For example, the real neutral rate is Source: IMF staff calculation currently about 1.4 percent, using the headline inflation instead of core inflation in the estimation. Based on these estimates, the current monetary policy stance is assessed to be broadly neutral.

D. Conclusions

9. The recent monetary policy tightening has brought the policy rate slightly above the estimated historical reaction function. This could be reflecting Bank of Mexico’s reaction to the significant uncertainty around the baseline inflation outlook, with notable upside risks related to the potential for materialization of second-round effects from the large exchange rate depreciation, the expected liberalization of gasoline prices, and a rebound in food prices.

2 In the reported estimates, the following standard error shocks were assumed: : 0.75, : 0.5, : 0.25, : 0.25 and : 0.125. 3 Since the estimation suggests that the shock z follows a near-random walk, the analysis focuses on the near-term dynamics of the neutral rate. Despite the possible unit root, the coefficient estimates are consistent, but the implied long-term steady state neutral interest (2.72) is not very informative.

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10. The monetary policy stance in Mexico has shifted from accommodative to broadly neutral. The estimated nominal neutral rate is about 3¾-4½ percent, just below the current policy rate. There is significant uncertainty around the estimated range for the neutral interest rate, although the finding that it has declined over time appears to be robust. It is also consistent with the literature, which finds a substantial decline in the neutral rate over time in many countries.

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References

Adjemian, Stéphane, Houtan Bastani, Michel Juillard, Frédéric Karamé, Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto and Sébastien Villemot, 2011, “Dynare: Reference Manual, Version 4”, Dynare Working Papers, No. 1, CEPREMAP.

Holston, Kathryn, Thomas Laubach, and John Williams, 2016, “Measuring the Natural Rate of Interest: International Trends and Determinants,” Federal Reserve Bank of San Francisco Working Papers, No. 2016-11.

Magud, Nicolas, and Evridiki Tsounta, 2012, “To Cut or Not to Cut? That is the (Central Bank’s) Question—In Search of the Neutral Interest Rate in Latin America,” IMF Working Papers, No. 12/243.

Pescatori, Andrea and Jarkko Turunen, 2015, “Lower for Longer: Neutral Rates in the United States,” IMF Working Papers, No. 15/135.

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